A note on second order Riesz transforms in 3-dimensional Lie groups

Fabrice Baudoin, Li Chen*

*Corresponding author af dette arbejde

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Abstract

We prove explicit Lp bounds for second order Riesz transforms of the sub-Laplacian and of the Laplacian in the Lie groups H, SU(2) , and SL~ (2). Our proof makes use of martingale transform techniques and specific commutation properties between the complex gradient and the sub-Laplacian in those Lie groups.

OriginalsprogEngelsk
TidsskriftARCHIV DER MATHEMATIK
Vol/bind118
Nummer3
Sider (fra-til)291-304
Antal sider14
ISSN0003-889X
DOI
StatusUdgivet - mar. 2022
Udgivet eksterntJa

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